The theory of $q$-rung orthopair fuzzy sets ($q$-ROFSs) proposed by Yager effectively describes fuzzy information in the real world. Because $q$-ROFSs contain the parameter $q$ and can adjust the range of expressed fuzzy information, they are superior to both intuitionistic and Pythagorean fuzzy sets. Archimedean T-norm and T-conorm (ATT) is an important tool used to generate operational rules based on the q-rung orthopair fuzzy numbers ($q$-ROFNs). In comparison, the Bonferroni mean (BM) operator has an advantage because it considers the interrelationships between the different attributes. Therefore, it is an important and meaningful innovation to extend the BM operator to the $q$-ROFNs based upon the ATT. In this paper, we first discuss $q$-rung orthopair fuzzy operational rules by using ATT. Furthermore, we extend BM operator to the $q$-ROFNs and propose the $q$-rung orthopair fuzzy Archimedean BM $(q\hbox{-}{ROFABM})$ operator and the q-rung orthopair fuzzy weighted Archimedean BM $(q\hbox{-}{ROFWABM})$ operator and study their desirable properties. Then, a new multiple-attribute decision-making (MADM) method is developed based on $q\hbox{-}{ROFWABM}$ operator. Finally, we use a practical example to verify effectiveness and superiority by comparing to other existing methods.

中文翻译：

---

基于q梯级正交模糊数阿基米德Bonferroni算子的多属性决策


Yager提出的$q$-rung orthopair模糊集（$q$-ROFSs）理论有效地描述了现实世界中的模糊信息。由于$q$-ROFS包含参数$q$并且可以调整表达模糊信息的范围，因此它们优于直觉模糊集和毕达哥拉斯模糊集。阿基米德 T-范数和 T-conorm (ATT) 是用于生成基于 q 梯级正交模糊数 ($q$-ROFNs) 的运算规则的重要工具。相比之下，Bonferroni 均值 (BM) 算子具有优势，因为它考虑了不同属性之间的相互关系。因此，基于ATT将BM算子扩展到$q$-ROFNs是一项重要且有意义的创新。在本文中，我们首先使用 ATT 讨论 $q$-rung 正交对模糊运算规则。此外，我们将 BM 算子扩展到 $q$-ROFN，并提出 $q$-rung 正交对模糊阿基米德 BM $(q\hbox{-}{ROFABM})$ 算子和 q-rung 正交对模糊加权阿基米德 BM $ (q\hbox{-}{ROFWABM})$ 运算符并研究它们所需的属性。然后，基于$q\hbox{-}{ROFWABM}$算子开发了一种新的多属性决策（MADM）方法。最后，我们用一个实际例子通过与其他现有方法的比较来验证有效性和优越性。